Smyth was injured Wednesday night in the second period of the Avs' 3-0 loss to the Phoenix Coyotes.
Smyth, who has 26 goals and 33 assists in 77 games, is the latest frontline player sidelined in Denver. Paul Stastny and Joe Sakic have missed chunks of the season.
Largely as a result of their injury epidemic, the Avs are mired in their worst season since the franchise moved from Quebec to Denver in 1995. They will finish below .500 for the first time since 1993-94, when they were the Nordiques. They've lost eight straight games, matching the franchise mark set in January 1992.
Stastny has been out since March 17 with a broken foot that may sideline him for the remainder of the season. He missed 26 games earlier this season with a broken forearm.
Sakic has missed most of the season with a series of injuries. He stuck his hand in a snow blower in December and needed emergency surgery. Then, he had back surgery to repair a herniated disk and hasn't been able to play because of weakness in his left leg.